An arch is in the shape of a parabola whose axis is vertically downwords and measures 80 mts across its boltom on the ground. Its highest point is 24 mts. The measure of the horizontal beam across its cross section at a height or 18 mts is

An arch is built so that it has the shape of a parabola with the equation y=-3x^(2)+24x where y represents the height of the arch in meters. How many times greater is the maximum height of the arch than the width of the arch at its base?

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is

A wedge as shown in figure has a rough curved surface of coefficient of kinetic friction (1)/sqrt(3) whose shape can be given by equation y=x^(2) , where the horizontal direction is x-axis, vertical direction as y axis and the end of surface O as origin and x & y are measured in meter. A small block is released, from a certain point on the surface. The maximum height of the point from where block should be released so that it does not slip.

A long wire in the shape of a cylindrical shell of inner and outer radii R/2 and R respectively carries a steady current I in a direction parallel to its length. This current is uniformly distributed across the area of cross-section of the wire. The magnetic field intensity at a point at a distance (3R)/4 from the axis of the wire is m((mu_(0)I)/(pi R)) .. The value of m is _________.

A particle is ejected from the tube at A with a velocity V at an angle theta with the verticle y-axis at a height h above the ground as shown. A strong horizontal wind gives the particle a constant horizontal acceleration a in the positive x-direction. If the particle strikes the ground at a point directly under its released position and the downward y-acceleration is taken as g then find h.

A unifrom rod AB of length 4m and mass 12 kg is thrown such that just after the projection the centre of mass of the rod moves vertically upwards with a velocity 10 m//s and at the same time its is rotating with an angular velocity (pi)/(2) rad//sec about a horizontal axis passing through its mid point. Just after the rod is thrown it is horizontal and is as shown in the figure. Find the acceleration (in m//sec^(2) ) of the point A in m//s^(2) when the centre of mass is at the highest point. (Take = 10 m//s^(2) and pi^(2) = 10 )

A thin uniform rod of mass M and length L is free to rotate in vertical plane about a horizontal axis passing through one of its ends. The rod is released from horizontal position shown in the figure. Calculate the shear stress developed at the centre of the rod immediately after it is released. Cross sectional area of the rod is A. [For calculation of moment of inertia you can treat it to very thin]

Pulfrich refractometer is used to measure the refractive index of solids and liquid. It consist of right angled prism. A having its two faces perfectly plane. One of the face is horizontal and the other is vertical as shown is figure. The solid B whose refractive index is to be determined is taken having two faces cut perpendicular to one another. Light is incident in a direction parallel to the horizontal surface so that the light entering the prism A is at critical angle C. Finally, it emerges from the prism at an angle i. Let the refractive index of the solid be mu and that of the prism A be mu_(0) (which is known). Here mu_(0)gtmu and by measuring i, mu can be determinged. Q. Refractive index of the solid (mu) in terms of mu_(0) and i is

A uniform rod AB of mass 3m and length 2l is lying at rest on a smooth horizontal table with a smooth vertical axis through the end A. A particle of mass 2m moves with speed 2u across the table and strikes the rod at its mid-point C if the impact is perfectly elastic. Find the speed of the particle after impact if (a). It strikes rod normally, (b). Its path before impact was inclinded at 60^(@) to AC.